Grade 12 Maths · Financial Maths

Use the future value formula

Use the future value formula for regular savings, for example find how much R500 saved every month grows to after 10 years.

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Future Value Grade 12 | IntroductionKevinmathscience

Future and Present Value Examples | Grade 12 Financial MathsKevinmathscience

Sinking Fund Gr 12 Financial MathsKevinmathscience

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Question 7.2 · May/June 2024 · Paper 1 · National (DBE) · 4 marks

Eric and Thandi need to save R80 000 each to go on a holiday at the end of December 2027.
- Thandi decides that she will start saving at the end of January 2025. She will make 36 monthly deposits into a savings account that pays interest at 8,6% p.a., compounded monthly. The deposit will be made at the end of each month.
- Eric calculates that if he makes 48 deposits of R1 402,31, starting at the end of January 2024, he will have enough money to go on holiday. He will make his deposits into a savings account at the end of each month. The savings account pays interest at 8,6% p.a., compounded monthly.

7.2 Calculate the difference between the total amount that Eric and Thandi will deposit into their respective savings accounts over the given period.(4)

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More past paper questions: use the future value formula

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3. Question WE5 · Siyavula Grade 12 Mathematics, 3.3 Future value annuities, Worked example 5 · 3 marks
WE5 Kosma is planning a trip to Canada to visit her friend in two years' time. She makes an itinerary for her holiday and she expects that the trip will cost R25 000. How much must she save at the end of every month if her savings account earns an interest rate of $10, 7%$ per annum compounded monthly?(3)
Show the memo (3 ticks)Memo
1. ✓
  Formula and values $F = \frac{x [ ( 1 + i ) ^{n} - 1 ]}{i}$ , so $x = \frac{F \times i}{[ ( 1 + i ) ^{n} - 1 ]}$
  $F = 25000$ ; $i = \frac{0 , 107}{12}$ ; $n = 2 \times 12 = 24$
  1 mark · Use the future value formula
2. ✓
  Substitution $x = \frac{25 000 \times \frac{0 , 107}{12}}{[ ( 1 + \frac{0 , 107}{12} ) ^{24} - 1 ]}$
  1 mark · Use the future value formula
3. ✓
  Answer $x = R 938, 80$
  Kosma must save R938,80 each month so that she can afford her holiday.
  1 mark · Use the future value formula
4. Question WE6 · Siyavula Grade 12 Mathematics, 3.3 Future value annuities, Worked example 6 · 3 marks
WE6 Simon starts to save for his retirement. He opens an investment account and immediately deposits R800 into the account, which earns $12, 5%$ per annum compounded monthly. Thereafter, he deposits R800 at the end of each month for $20$ years. What is the value of his retirement savings at the end of the $20$ year period?(3)
Show the memo (3 ticks)Memo
1. ✓
  Formula and values $F = \frac{x [ ( 1 + i ) ^{n} - 1 ]}{i}$
  $x = 800$ ; $i = \frac{0 , 125}{12}$ ; $n = 1 + (20 \times 12) = 241$
  1 mark · Use the future value formula
2. ✓
  Substitution $F = \frac{800 [ ( 1 + \frac{0 , 125}{12} ) ^{241} - 1 ]}{\frac{0 , 125}{12}}$
  1 mark · Use the future value formula
3. ✓
  Answer $F = R 856415, 66$
  Simon will have saved R856 415,66 for his retirement.
  1 mark · Use the future value formula
5. Question c · Siyavula Grade 12 Mathematics, 3.3 Future value annuities, Worked example 7 · 3 marks
Wellington Courier Company buys a delivery truck for R296 000. The value of the truck depreciates on a reducing-balance basis at $18%$ per annum. The company plans to replace this truck in seven years' time and they expect the price of a new truck to increase annually by $9%$ .
c Calculate the required monthly deposits if the sinking fund earns an interest rate of $13%$ per annum compounded monthly.(3)
Show the memo (3 ticks)Memo
1. ✓
  Formula and values $x = \frac{F \times i}{[ ( 1 + i ) ^{n} - 1 ]}$
  $F = 467311, 08$ ; $i = \frac{0 , 13}{12}$ ; $n = 7 \times 12 = 84$
  1 mark · Use the future value formula
2. ✓
  Substitution $x = \frac{467 311 , 08 \times \frac{0 , 13}{12}}{[ ( 1 + \frac{0 , 13}{12} ) ^{84} - 1 ]}$
  1 mark · Use the future value formula
3. ✓
  Answer $x = R 3438, 77$
  The company must deposit R3 438,77 each month.
  1 mark · Use the future value formula
6. Question a · Siyavula Grade 12 Mathematics, 3.3 Future value annuities, Worked example 4 · 3 marks
Ciza decides to start saving money for the future. At the end of each month she deposits R900 into an account at Harringstone Mutual Bank, which earns $8, 25%$ interest p.a. compounded monthly.
a Determine the balance of Ciza's account after $29$ years.(3)
Show the memo (3 ticks)Memo
1. ✓
  Formula and values $F = \frac{x [ ( 1 + i ) ^{n} - 1 ]}{i}$
  $x = 900$ ; $i = \frac{0 , 0825}{12}$ ; $n = 29 \times 12 = 348$
  1 mark · Use the future value formula
2. ✓
  Substitution $F = \frac{900 [ ( 1 + \frac{0 , 0825}{12} ) ^{348} - 1 ]}{\frac{0 , 0825}{12}}$
  1 mark · Use the future value formula
3. ✓
  Answer $F = R 1289665, 06$
  1 mark · Use the future value formula

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